The vertical negative muon stopping rate at depths 0.35--1000 hg/cm2 of standard rock has been evaluated by means of a Monte Carlo simulation of the muon transport underground. The muon energy losses take into account both continuous (ionization and pair production) and stochastic (bremmstrahlung and nuclear interaction) processes. The dependence of the charge ratio μ+/μ- on the muon momentum is included. The effect of muon multiple scattering has been estimated. Results are given both for high-latitude and equatorial sites, and they are compared to previous calculations and to experimental data. ¿ American Geophysical Union 1989